Vernier for slide rules



July 29, 1947. E, sEmMAN 2,424,713

VERNIER FOR SLIDE RULES Filed nay 1i, 1946 Ill/11111,.

' /-vENroR.- EM/L SE/DMA/v Patented July 29, 1947 UNITED STATES PATENT OFFICE 9 Claims. (Cl. 23S-70) This invention relates to verniers and particularly to a slidable accessory adaptable for use on conventional slide rules or similar scaled instruments.

The primary object of this invention is to provide a Vernier of the type stated that is adaptable for use with, and which may be easily mounted on, a conventional slide rule and which will enable the accurate reading of an additional place or digit. K

Another object of this invention is to provide a Vernier that is movable at right angles to the underlying main scale.

A further object is to provide a transparent Vernier plate the indicia of which are visible together with the main scale through the cursor or indicator.

Still another object is to provide a device of the type stated which is easy to read and interpret, and which requires no extraneous apparatus for its operation.

These and other objects of the invention will become apparent from a reading of the following speciflcation and claims, together with the accompanying drawing in which like parts are referred to and indicated by like reference char' acters and wherein:

Figure 1 is a top plan View of the right portion of a conventional slide rule having the Vernier mounted thereon;

Figure 2 is a longitudinal cross-sectional View of the same taken along th'e line and in the direction of the arrows 2-2 of the Figure 1;

Figure 3 is a transverse cross-sectional View of the same taken along the line and in the direction of the arrows 3 3 of the Figure 1;

Figure 4 is an enlarged view of a portion of the Vernier and slide rule as illustrated in the Figure 1;

Figure 5 is a perspective View of the Vernier in its preferred form;

Figure 6 is a perspective View of an alternate form of the Vernier; and

Figure 7 is a top plan View of the Vernier attached to a conventional caliper.

The instant invention consists broadly of the plate 3|, having indicia thereon, and th'e guide pieces 32, which together form the Vernier 30 as illustrated in the Figures 5 and 6, and which is shown in Figure 1 as it appears mounted on a conventional logarithmic slide rule I0.

The slide rule consists of two stationary rails having inner edges I3 and a movable rail I5 mounted therebetween having edges which slidably abut the edges I3. Said rail |5 being capable of longitudinal sliding movement with' reference to the stationary rails Il, by reason of the tongue and groove construction of the slide rule as shown in Figure 3.

The stationary rails II have the conventional A and D scales I2 along their edges I3. The movable rail I5 has the conventional B and C scales I6 along its edges II, and the inverted CI scale in the center, as shown in Figure 1. At 20 there is shown a cursor herein referred to as an indicator, in th'at itis the common trade term used for such devices.

This indicator is slidable longitudinally of the rails I I and I5, and consists of a glass plate 22 mounted on the end pieces 2| which have tongues which slidably engage grooves in the outer faces of the rails II as shown in Figure 3.

The glass plate 22 has parallel side edges 26, and a central Vertical hair-line '24 which is used for the purpose of reading the relative positions of the movable and fixed scales I6 and I2. The screws 23 attach the glass 22 to the end pieces 2 I, While the flat spring 25 holds the indicator in slight frictional contact with the fixed rails I I, and square with the various scales. The Vernier 30 consists of a thin sheet of rigid transparent material such' as glass or other transparent material approximately 1%" wide, and long enough to extend the Width of the indicator plate 22, and then connect with the guide piece 32.

When attached to a slide rule the Vernier is placed so that its plate 3| is under the indicator glass 22 and above the scale faces I2 and I6 with the guides 32 extending vertically from the ends of the plate 3| to hold the Vernier in sliding contact with the indicator plate edges 26 as shown in Figures 1, 2 and 3. The guide pieces 32 act as runners which slide along the parallel side edges of the indicator glass 22, and carrythe Vernier plate up and down the indicator at right angles to the path of travel of the indicator as indicated in Figure 1, where the Vernier 30 is shown in an alternate position 30a.

In its preferred form the indicia on the Vernier plate 3|, as illustrated in Figure 5, consists of a short oblique line 34, and a long oblique line 35, drawn so that their point of intersection d is, and will always remain during movement, on the indicator hair-line 24.

A third line 33 is drawn across the plate 3| thru the point d, and perpendicular to its longitudinal edges 36. This line is added for the sake of convenience in aligning the point d with the hair-line 24, since the point d must lie on the hair-line 24 if the line 33 is made to coincide with the hair-line 24. However, this line may be omitted without aiTecting the operation of the Vernier.

The three lines 33, 34, and 35 shown in Figure 5 have imaginary points a, b, and c which lie in a straight line perpendicular to hair line 24.

The lines 33, 34, and 35 together with the imaginary line ac drawn through the points a, b, and c form two right triangles abd and ebd, and a third large triangle adc.

The lines 34 and 35 are drawn at such an angle to the line 33 that the length of the base ab of the triangle and will bear a predetermined ratio to the length of the base ac of the triangle adc.

When used with a logarithmic slide rule the most convenient ratio has been found to be 1:10 since this will give readings in tenths of the smallest scale division. However, any ratio found to be most convenient for the use intended may be employed.

The ratio illustrated here may be stated as follows If a second line should be drawn to intersect lines 33, 34, and 35 parallel to the line abc, the new triangles formed will have angles equal to the angles of the original triangles, and therefore the new triangles will be similar to the original triangles, and the lengths of their base sides will bear the same ratio to each other as those of the original triangles, namely, 1: 10.

In other words, irrespective of the location of the lines drawn to intersect the lines 33, 34, and 35 parallel to the original line abc, the ratio of the lengths of the new bases a'b to ac' will always be 1: 10, or a constant.

By placing the Vernier on the slide rule indicator in such a manner that the edge I3 of one of the scales I2 becomes the line abc, we can put this knowledge to practical use in accuratelir determining the location of the indicator hairline when it lies between two scale divisions as illustrated in Figure 4.

When using a conventional slide rule as illustrated in Figure 1 we read four figures of a result on one part of the scale, and three iigures on the remaining part. These figures can be accurately read on the scale division lines only. If the reading, as represented by the hair-line 24, falls between scale divisions the number has to be estimated as being a certain percentage of the distance from the next preceding scale division to the next following scale division. However', the location of the hair-line can be accurately determined by the use of this Vernier in the following manner.

The Figure l shows a slide rule with a reading indicated somewhere between 4.00 and 4.05 which is shown for greater convenience in enlarged form in Figure 4.

The indicator hair-line 24 is shown intersecting the scale I2 at a point y on its edge I3. The point y is somewhere between the reading 4.00 and 4.05. The problem is to nd out where. The Vernier 30 is moved along the indicator at right angles to the scale edge I3, with the Vernier hair-line 33 coinciding with the indicator hairline 24 until the line 34 intersects the scale division next preceding the position of the hairline 24, at the point :c on the scale edge I3. The line 35 will then intersect the scale edge I3 at a point 2.

We now have a set up for our Vernier which uses the edge I3 to form a line which runs through point s: on the scale, which we will call point a on the line 34; point y on the scale, which we will call point b on line 33; and point e on the scale, which we will call point c on line 35.

From our previous discussion we know that By looking at Figure 4, we can see that the distance from a to c is six scale divisions, therefore, by substitution in the above equation we have Since ab on the Vernier is the same as ry on the scale edge I3, we no-w know that the point y on the scale edge I3 represents 0.6 of the distance between the point or the scale division marked 4.00,. and the next following scale division marked 4.05. Since 0.6 0.05=0.03, and the hair-line 24 is beyond the scale division 4.00, the correct reading must be 4.00 plus 0.03 or 4.03.

Another and quicker way of arriving at the same answer is to take the scale reading at a and subtract it from the reading at c, then multiply the difference by the constant, which in this CaSe is and add the product t0 the reading at a (4.30 minus 4.00) X-ll-O: 0.03

4.00 plus 0.03::403 which is the exact reading indicated by the hair-line 24 in Figure 4.

When used with scales having equally spaced division marks the lines 34 and 35 are straight lines, but with scales having unequally spaced di- Vision marks, such as a logarithmic scale, the true path of the line 35 is a curve as shown at 35a. However, this curve deviates so little from a straight line when used with a conventional ten inch slide rule, that it can be very closely approximated by a straight line.

If we wish to get a still closer approximation, we may modify the indicia onl the plate 3| by using two pair of oblique lines as shown in Figure 6. One of the pair will be used as before, but only for the first half of the distance between scale divisions such as the distance between 4.00 and 4.025, if we use the same hairline position as illustrated in Figure 4; and the inverted pair to be used for reading the second half oi the distance, or the distance between 4.025 and 4.05.

In using the inverted pair the short inverted oblique line of the Vernier is made to intersect the next scale division following the hair-line 24, which would be 4.05 in this oase, and then subtracting the value found which would be 0.02 from 4.05 to give the answer 4.03.

Another modified form of indicia has the short oblique lines 34a, on the same side of the hairline 33 as the long oblique line 35, as shown in Figure 5. The point a now falls to the right of b since the line 34a is to the right of the line 33.

The line 34a is made to intersect the next scale division following the location of the hair-line 24 and the same equation is used:

abl

However, the result is subtracted from the reading at point a since that is a reading of a scale division beyond the location of the hair-line 24.

The Vernier may be used to read the hair-line position in combination wtih other scales on the slide rule, as indicated by the other position of the Vernier on the indicator, as shown at 30a in Figure 1.

This type of Vernier may be used with any instrument employing a scale, and is not to be thought of as being confined to use with slide rules. A modified form of this Vernier is shown in Figure 7, attached to a conventional caliper 50, having a scale 55 and a sliding jaw 5l. 'I'he vernier 52 has the characteristic short oblique line 53, and the long oblique line 54, and is capable of being moved at right angles to the scale 55 in order to take a reading.

It will now be clear that there is provided a device which accomplishes the objectives heretofore set forth. While the invention has been disclosed in its preferred form, it is to be understood that the specific embodiment thereof as described and illustrated herein is not to be considered in a limited sense as there may be other forms or modications of the invention which should also be construed to come within the scope of the appended claims.

I claim:

1. In combination with a slide rule of the type having a set of opposed linear graduations and a cursor thereon, a plate slidably engageable with the aforesaid cursor, the said plate having indicia thereon, the said indicia consisting of a pair of lines intersecting on a line on the cursor and intercepting a segment of the opposed linear graduations.

2. In combination with a slide rule of the type having a set of opposed linear graduations at abutting edges thereof and including a movable indicator having a hair-line thereon, a plate slidably engageable with the aforesaid indicator, the said plate having a pair of oblique lines thereon capable of forming together with the aforesaid abutting edges and the hair-line two right triangles.

3. In combination with a slide rule of the type having a set of opposed linear graduations at abutting edges thereof and including a, movable indicator having a hair-line thereon, a plate slidably engageable with the aforesaid indicator, the said plate having a pair of oblique lines thereon capable of forming together with the aforesaid abutting edges and the hair-line two right triangles, and guide means on the said plate engageable with the indicator.

4. In combination with a slide rule of the type having a set of opposed linear graduations and a cursor thereon, a plate slidably engageable with the aforesaid cursor, the said plate having indicia thereon, the said indicia consisting of a pair of lines intersecting on a line on the cursor and intercepting a segment of the opposed linear graduations, and guide means on the said plate engageable with the cursor.

5. In combination with a slide rule of the type having two or more sets of opposed linear graduations and a transparent indicator, having a hairline engraved thereon, slidably engaged therewith and capable of longitudinal motion with reference to the said linear graduations, a Vernier comprising, a movable plate slidably engaged with the aforesaid indicator, said plate having indicia inscribed thereon consisting of two intersecting lines capable of intercepting a segment of the said linear graduations and intersecting at a point lying on the aforesaid indicator line.

6. In combination with a slide rule of the type having two or more sets of opposed linear graduations and a transparent indicator, having a hairline engraved thereon, slidably engaged therewith and capable of longitudinal motion with reference to the said linear graduations, a vernier comprising, a movable plate slidably engaged with the aforesaid indicator, said plate having indicia inscribed thereon consisting of two intersecting lines capable of intercepting a segment of the said linear graduations and intersecting at a point lying on the aforesaid indicator line, said indicia lines making unequal angles with the said indi-y cator line.

7. In combination with a slide rule of the type having two or more sets of opposed linear graduations and a transparent indicator, having a hair-line engraved thereon, slidably engaged therewith and capable of longitudinal motion with reference to the said linear graduations, a Vernier, comprising in combination, a transparent plate member slidably mounted on said indicator and movable at right angles to the movement of the indicator, said plate having indicia inscribed thereon consisting of two intersecting lines capable of intercepting a segment of the said linear graduations and intersecting at a point lying on the aforesaid indicator line, and guide members attached to and integral with said plate member and capable of holding said plate member in fixed slidable relation with the aforesaid indicator hairline.

8. A vernier of the type defined in claim 7 and further characterized by the transparent plate having a third line inscribed thereon drawn from the point of intersection of the first two lines, perpendicular to the segment of the linear graduations intercepted by the said lines.

9. A vernier of the type defined in claim 7 and further characterized by the length of the segment of the linear graduations intercepted by the two intersecting lines having a definite known ratio to the length of the segment intercepted by one of the said lines and the aforesaid indicator line.

EMIL SEIDMAN. 

